CK-12-Basic Probability and Statistics Concepts - A Full Course

6.2. Variance of a Data Set http://www.ck12.org

μ=

∑x

n

=

1 , 316. 1

18

≈ 73. 1

σ^2 =

∑(x−μ)^2

n

σ^2 =

14 , 016

18

≈ 778. 66

The variance of the data set is approximately 778.66 mm.

Therefore, the data values for the precipitation are more variable. This is indicated by the large variance of the data
set.

Guided Practice

A consumer advocacy magazine wants to compare 2 brands of incandescent lamps. The magazine took samples
of each brand, with each sample consisting of 10 lamps. All of the lamps in both of the samples were allowed to
burn as long as they could, and the times were recorded in hours. The following are the results obtained from the
magazine. Calculate the variance of the samples of the 2 brands of incandescent lamps. Which brand has the more
variable burning times?

TABLE6.6:

Brand A (Time in hours) Brand B (Time in hours)

760 820

790 900

800 810

780 790

850 810

790 800

750 850

820 820

810 920

800 890

Answer:

Brand A

TABLE6.7:

x (x−x ̄) (x−x ̄)^2

760 − 35 1,225

790 − 5 25

800 5 25

780 − 15 225

850 55 3,025

790 − 5 25

750 − 45 2,025

820 25 625

810 15 225

800 5 25